With a TS EAPCET rank of 40,000, your chances of securing a seat in NIMS University, particularly for popular courses like Computer Science Engineering (CSE), are quite slim. The cutoffs for CSE at NIMS and similar colleges tend to be much lower, often around the 25,000 mark or better for general categories.

However, the final availability of seats may vary depending on the specific counseling phase and category (General, BC, SC, ST). Generally, as per previous trends, the competition for CSE seats is high, and many candidates with ranks significantly lower than yours may still not secure a seat.

If you're specifically interested in NIMS or similar institutions, it would be beneficial to consider alternative courses that may have higher availability or lower cutoff ranks. You could also explore other colleges that may be less competitive in terms of cutoff ranks for the same program.

For the most accurate and updated information regarding available seats and cutoffs, it's advisable to check the official TS EAPCET counseling website or consult with the admissions office at NIMS.